Note 13 — PHYSIOGNOMY OF PLANTS.

p. 17.—“Species of phænogamous plants already contained in herbariums.”

We must carefully distinguish between three different questions: How many species of plants are described in printed works? how many have been discovered, i. e. are contained in herbariums, though without being described? how many are probably existing on the globe? Murray’s edition of the Linnean system contains, including cryptogamia, only 10042 species. Willdenow, in his edition of the Species Plantarum, between the years 1797 and 1807, had already described 17457 phænogamous species, (from Monandria to Polygamia diœcia.) If we add 3000 cryptogamous species, we obtain the number which Willdenow mentions, viz. 20000 species. More recent researches have shown how much this estimation of the number of species described and contained in herbariums falls short of the truth. Robert Brown counted above 37000 phænogamous plants. (General Remarks on the Botany of Terra Australis, p. 4.) I afterwards attempted to give the geographical distribution (in different parts of the earth already explored), of 44000 phænogamous and cryptogamous plants. (Humboldt, de distributione geographica Plantarum, p. 23.) Decandolle found, in comparing Persoon’s Enchiridium with his Universal System in 12 several families, that the writings of botanists and European herbariums taken together might be assumed to contain upwards of 56000 species of plants. (Essai élementaire de Géographie botanique, p. 62.) If we consider how many species have since that period been described by travellers,—(my expedition alone furnished 3600 of the 5800 collected species of the equinoctial zone),—and if we remember that in all the botanical gardens taken together there are certainly above 25000 phænogamous plants cultivated, we shall easily perceive how much Decandolle’s number falls short of the truth. Completely unacquainted as we still are with the larger portions of the interior of South America,—(Mato-Grosso, Paraguay, the eastern declivity of the Andes, Santa Cruz de la Sierra, and all the countries between the Orinoco, the Rio Negro, the Amazons, and Puruz),—of Africa, Madagascar, Borneo, and Central and Eastern Asia,—the thought rises involuntarily in the mind that we may not yet know the third, or probably even the fifth part of the plants existing on the earth! Drège has collected 7092 species of phænogamous plants in South Africa alone. (See Meyer’s pflanzen geographische Documente, S. 5 and 12.) He believes that the Flora of that district consists of more than 11000 phænogamous species, while on a surface of equal area (12000 German, or 192000 English square geographical miles) von Koch has described in Germany or Switzerland 3300, and Decandolle in France 3645 species of phænogamous plants. I would also recall that even now new Genera, (some even consisting of tall forest trees), are being discovered in the small West Indian Islands which have been visited by Europeans for three centuries, and in the vicinity of large commercial towns. These considerations, which I propose to develop in further detail at the close of the present annotation, make it probable that the actual number of species exceeds that spoken of in the old myth of the Zend-Avesta, which says that “the Primeval Creating Power called forth from the blood of the sacred bull 120000 different forms of plants!”

If, then, we cannot look for any direct scientific solution of the question of how many forms of the vegetable kingdom,—including leafless Cryptogamia (water Algæ, funguses, and lichens), Characeæ, liver-worts, mosses, Marsilaceæ, Lycopodiaceæ, and ferns,—exist on the dry land and in the ocean in the present state of the organic life of our globe, we may yet attempt an approximate method by which we may find some probable “lowest limits” or numerical minima. Since 1815, I have sought, in arithmetical considerations relating to the geography of plants, to examine first the ratios which the number of species in the different natural families bear to the entire mass of the phænogamous vegetation in countries where the latter is sufficiently well known. Robert Brown, the greatest botanist among our cotemporaries, had previously determined the numerical proportions of the leading divisions of the vegetable kingdom; of Acotyledons (Agamæ, Cryptogamic or cellular plants) to Cotyledons (Phanerogamic or vascular plants), and of Monocotyledonous (Endogenous) to Dicotyledonous (Exogenous) plants. He finds the ratio of Monocotyledons to Dicotyledons in the tropical zone as 1 : 5, and in the cold zones of the parallels of 60° N. and 55° S. latitude, as 1 : 2½. (Robert Brown, General Remarks on the Botany of Terra Australis, in Flinders’ Voyage, vol. ii. p. 338.) The absolute number of species in the three leading divisions of the vegetable kingdom are compared together in that work according to the method there laid down. I was the first to pass from these leading divisions to the divisions of the several families, and to consider the ratio which the number of species of each family bears to the entire mass of phænogamous plants belonging to a zone of the earth’s surface. (Compare my memoir entitled De distributione geographica Plantarum secundum cœli temperiem et altitudinem montium, 1817, p. 24-44; and the farther development of the subject of these numerical relations given by me in the Dictionnaire des Sciences naturelles, T. xviii. 1820, p. 422-436; and in the Annales de Chimie et de Physique, T. xvi. 1821, p. 267-292.)

The numerical relations of the forms of plants, and the laws observed in their geographical distribution, may be considered in two very different ways. If plants are studied in their arrangement according to natural families, without regard to their geographical distribution, it is asked, What are the fundamental forms or types of organisation to which the greatest number of species correspond? Are there on the entire surface of the earth more Glumaceæ than Compositæ? Do these two orders make up between them one-fourth part of the whole number of phænogamous plants? What is the proportion of Monocotyledons to Dicotyledons? These are questions of General Phytology, or of the science which investigates the organisation of plants and their mutual connection, or the present state of the entire vegetable world.

If, on the other hand, the species of plants which have been grouped according to the analogy of their structure are considered, not abstractedly, but according to their climatic relations, or according to their distribution over the surface of the earth, we have questions offering quite another and distinct interest. We then examine what are the families which prevail more in proportion to other Phanerogamæ in the torrid zone than towards the polar circle? Are Compositæ more numerous, either in the same geographical latitudes or on the same isothermal lines, in the New than in the Old Continent? Do the forms which gradually lose their predominance in advancing from the equator towards the poles follow a similar law of decrease in ascending mountains situated in the equatorial regions? Do the proportions of particular families to the whole mass of Phanerogamæ differ in the temperate zones, and on equal isothermal lines, north and south of the equator? These questions belong properly to the Geography of Plants, and connect themselves with the most important problems of meteorology and terrestrial physics. The character of a landscape or country is also in a high degree dependent on the predominance of particular families of plants, which render it either desolate or adorned, smiling or majestic. Grasses forming extensive savannahs, Palms and other trees affording food, or social Coniferæ forming forests, have powerfully influenced nations in respect to their material condition, to their manners, to their mental dispositions, and to the more or less rapid development of their prosperity.

In studying the geographical distribution of forms, we may consider species, genera, and natural families, separately. In social plants, a single species often covers extensive tracts of country; as in northern regions forests of Pines or Firs and extensive heaths (ericeta), in Spain cistus-covered grounds, and in tropical America assemblages of the same species of Cactus, Croton, Brathys, or Bambusa Guadua. It is interesting to examine these relations more closely, and to view in one case the great multiplicity of individuals, and in another the variety of organic development. We may inquire what species produces the greatest number of individuals in a particular zone, or we may ask which are the families to which, in different climates, the greatest number of species belong. In a high northern region, where the Compositæ and the Ferns are to the sum of all the phænogamous plants in the ratio of 1 : 13 and 1 : 25 (i. e. where these ratios are found by dividing the sum total of all the Phanerogamæ by the number of species belonging to the family of Compositæ or to that of Filices or Ferns), it may nevertheless happen that a single species of fern covers ten times more ground than do all the species of Compositæ taken together. In this case Ferns predominate over Compositæ by their mass, or by the number of individuals belonging to the same species of Pteris or Polypodium; but they do not so predominate if we only compare the number of the different specific forms of Filices and Compositæ with the sum of all the phænogamous plants. Since, then, multiplication of plants does not follow the same law in all species,—that is to say, all species do not produce the same number of individuals,—therefore the quotients given by dividing the sum of the phænogamous plants by the number of species belonging to one family, do not suffice by themselves to determine the character of the landscape, or the physiognomy which Nature assumes in different regions of the earth. If the attention of the travelling botanist is engaged by the frequent repetition of the same species, their mass, and the uniformity of vegetation thus produced, it is even more arrested by the rarity or infrequency of several other species which are valuable to mankind. In tropical regions, where the Rubiaceæ, Myrtaceæ, Leguminosæ, or Terebinthaceæ, form forests, one is astonished to find the trees of Cinchona, particular species of Swietenia (Mahogany), Hæmatoxylon, Styrax, and balsamic Myroxylum, so sparingly distributed. We had occasion, on the declivities of the high plains of Bogota and Popayan, and in the country round Loxa, in descending towards the unhealthy valley of the Catamayo and to the Amazons River, to remark the manner in which the trees which furnish the precious fever-bark (species of Cinchona) are found singly and at considerable distances from each other. The China Hunters, Cazadores de Cascarilla (the name given at Loxa to the Indians and Mestizoes who collect each year the most efficacious of all fever-barks, that of the Cinchona Condaminea, among the lonely mountains of Caxanuma, Uritusinga, and Rumisitana), climb, not without peril, to the summits of the loftiest forest trees in order to gain a wide prospect, and to discern the solitarily scattered slender aspiring trunks of the trees of which they are in search, and which they recognise by the shining reddish tint of their large leaves. The mean temperature of this important forest region, situated in 4° to 4½° S. lat. and at an elevation of about 6400 to 8000 English feet, is from 12½° to 16° Réaumur (60°·2 to 68° Fahr.) (Humboldt and Bonpland, Plantes équinoxiales, T. i. p. 88, tab. 10.)

In considering the distribution of species, we may also proceed, without regard to the multiplication of individuals, to the masses which they form or the space which they occupy, and may simply compare together the absolute number of species belonging to a particular family in each country. This is the mode of comparison which Decandolle has employed in the work entitled Regni vegetabilis Systema naturale (T. i. p. 128, 396, 439, 464, and 510), and Kunth has carried it out in regard to the whole number of species of Compositæ at present known (above 3300). It does not show which is the predominant family either in the number of species or in the quantity of individuals as compared with other families; it merely tells how many of the species of one and the same family are indigenous in each country or each quarter of the world. The results of this method are on the whole more exact, because they are obtained by the careful study of single families without the necessity of being acquainted with the whole number of the phanerogamæ belonging to each country. The most varied forms of Ferns, for example, are found between the tropics; it is there, in the tempered heat of moist and shaded places in mountainous islands, that each genus presents the largest number of species: this variety of species in each genus diminishes in passing from the tropical to the temperate zone, and decreases still farther in approaching nearer to the pole. Nevertheless, as in the cold zone—in Lapland, for example—those plants succeed best which can best resist the cold, so the species of Ferns, although the absolute number is less than in France or Germany, are yet relatively more numerous than in those countries; i. e. their number bears a greater proportion to the sum total of all the phanerogamous plants of the country. These proportions or ratios, given as above-mentioned by quotients, are in France and Germany ¹⁄₇₃ and ¹⁄₇₁, and in Lapland ¹⁄₂₅. I published numerical ratios of this kind,—(i. e. the entire quantity of phænogamous plants in each of the different Floras divided by the number of species in each family)—in my Prolegomenis de distributione geographica Plantarum, in 1817; and in the Memoir on the distribution of plants over the Earth’s surface, subsequently published in the French language, I corrected my previously published numbers by Robert Brown’s great works. In advancing from the Equator to the Poles, the ratios taken in this manner vary considerably from the numbers which would be obtained from a comparison of the absolute number of species belonging to each family. We often find the value of the fraction increase by the decrease of the denominator, while yet the absolute number of species has diminished. In the method by fractions, which I have followed as more instructive in reference to the geography of plants, there are two variables; for in proceeding from one isothermal line, or one zone of equal temperature, to another, we do not see the sum total of all the phanerogamæ change in the same proportion as does the number of species belonging to a particular family.

We may, if we please, pass from the consideration of species to that of divisions formed in the natural system of botany according to an ideal series of abstractions, and direct our attention to Genera, to Families, and even to the still higher, i. e. more comprehensive, Classes. There are some genera, and even some entire families, which belong exclusively to particular zones of the Earth’s surface; and this not only because they can only flourish under a particular combination of climatic conditions, but also because both the localities in which they originated, and their migrations, have been limited. It is otherwise with the greater number of genera and of families, which have their representatives in all regions of the globe, and at all latitudes of elevation. The earliest investigations into the distribution of vegetable forms related solely to genera; we find them in a valuable work of Treviranus, in his Biology (Bd. ii. S. 47, 63, 83, and 129). This method is, however, less fitted to afford general results than that which compares either the number of species of each family, or the great leading divisions (of Acotyledons, Monocotyledons, and Dicotyledons) with the sum of all the phanerogamæ. We find that in the cold zones the variety of forms does not decrease so much if estimated by genera as if estimated by species; in other words, we find relatively more genera and fewer species. (Decandolle, Théorie élémentaire de la Botanique, p. 190; Humboldt, Nova genera et species Plantarum, T. i pp. xvi. and 1.) It is almost the same in the case of high mountains whose summits support single members of a large number of genera, which we should have been à priori inclined to regard as belonging exclusively to the vegetation of the plains.

I have thought it desirable to indicate the different points of view from which the laws of the geographical distribution of plants may be considered. It is by confounding these different points of view that apparent contradictions are found; which are unjustly attributed to uncertainties of observation. (Jahrbücher der Gewächskunde, Bd. i Berlin, 1818, S. 18, 21, 30.) When such expressions as the following are made use of—“This form, or this family, diminishes as the cold zones are approached;—it has its true home in such or such a latitude;—it is a southern form;—it predominates in the temperate zone;” care should always be taken to state expressly whether the writer is speaking of the absolute number of species, and its increase or decrease with the change of latitude; or whether he means that the family in question prevails over other families of plants as compared with the entire number of phanerogamæ of which a Flora consists. The impression of prevalence as conveyed by the eye depends on relative quantity.

Terrestrial physics have their numerical elements, as has the System of the Universe, or Celestial Physics, and by the united labours of botanical travellers we may expect to arrive gradually at a true knowledge of the laws which determine the geographical and climatic distribution of vegetable forms. I have already remarked that in the temperate zone the Compositæ (Synanthereæ), and the Glumaceæ (including under this latter name the three families of Grasses, Cyperoidæ and Juncaceæ), make up the fourth part of all phænogamous plants. The following numerical ratios are the results of my investigations for 7 great families of the vegetable kingdom in the same temperate zone.

Glumaceæ ¹⁄₈ (Grasses alone ¹⁄₁₂) Compositæ ¹⁄₈ Leguminosæ ¹⁄₁₈ Labiatæ ¹⁄₂₄ Umbelliferæ ¹⁄₄₀ Amentaceæ (Cupuliferæ, Betulineæ, and Salicineæ) ¹⁄₄₅ Cruciferæ ¹⁄₁₉

The forms of organic beings are in reciprocal dependence on each other. In the unity of nature these forms limit each other according to laws which are probably attached to periods of long duration. If on any particular part of the globe we know with accuracy the number of species of one of the great families of Glumaceæ, Leguminosæ, or Compositæ, we may with a tolerable degree of probability form approximative inferences, both as to the sum of all the phanerogamæ of the country, and also as to the number of species belonging to the rest of the leading families of plants. The number of Cyperoidæ determines that of Compositæ, and the number of Compositæ that of Leguminosæ; they even enable us to judge in what classes or orders the Floras of countries are still incomplete, and teach us, if we are on our guard against confounding together very different systems of vegetation, what harvest may still remain to be reaped in the several families.

The comparison of the numerical ratios of families in different already well explored zones, has conducted me to the recognition of laws according to which, in proceeding from the equator to the poles, the vegetable forms constituting a natural family decrease or increase as compared with the whole mass of phanerogamæ belonging to each zone. We have here to regard not only the direction of the change (whether an increase or a decrease), but also its rapidity or measure. We see the denominator of the fraction which expresses the ratio increase or decrease: let us take as our example the beautiful family of Leguminosæ, which decreases in going from the equinoctial zone towards the North Pole. If we find its proportion or ratio for the torrid zone (from 0° to 10° of latitude) at ¹⁄₁₀, we obtain for the part of the temperate zone which is between 45° and 52° latitude ¹⁄₁₈, and for the frigid zone (lat. 67° to 70°) only ¹⁄₃₅. The direction followed by the great family of Leguminosæ (increase on approaching the equator), is also that of the Rubiaceæ, the Euphorbiaceæ, and especially the Malvaceæ. On the contrary, the Grasses and Juncaceæ (the latter still more than the former), diminish in approaching the equator, as do also the Ericeæ and Amentaceæ. The Compositæ, Labiatæ, Umbelliferæ, and Cruciferæ, decrease in proceeding from the temperate zone, either towards the pole or towards the equator, the Umbelliferæ and Cruciferæ decreasing most rapidly in the last-named direction; while at the same time in the temperate zone the Cruciferæ are three times more numerous in Europe than in the United States of North America. On reaching Greenland the Labiatæ have entirely disappeared with the exception of one, and the Umbelliferæ with the exception of two species; the entire number of phænogamous species, still amounting, according to Hornemann, to 315 species.

It must be remarked at the same time that the development of plants of different families, and the distribution of vegetable forms, does not depend exclusively on geographical, or even on isothermal latitude; the quotients are not always on the same isothermal line in the temperate zone, for example, in the plains of North America and those of the Old Continent. Within the tropics there is a very sensible difference between America, India, and the West Coast of Africa. The distribution of organic beings over the surface of the earth does not depend wholly on thermic or climatic relations, which are of themselves very complicated, but also on geological causes almost unknown to us, belonging to the original state of the earth, and to catastrophes which have not affected all parts of our planet simultaneously. The large pachydermatous animals are at the present time wanting in the New Continent, while we still find them in analogous climates in Asia and Africa. These differences ought not to deter us from endeavouring to search out the concealed laws of nature, but should rather stimulate us to the study of them through all their intricacies.

The numerical laws of the families of plants, the often striking agreement of the numbers expressing their ratios, where yet the species of which the families consist are for the most part different, conduct us into the mysterious obscurity which envelopes all that is connected with the fixing of organic types in the species of plants and animals, or with their original formation or creation. I will take as examples two adjoining countries which have both been thoroughly explored—France and Germany. In France, many species of Grasses, Umbelliferæ and Cruciferæ, Compositæ, Leguminosæ, and Labiatæ, are wanting which are common in Germany; and yet the numerical ratios of these six great families are almost identical in the two countries, as will be seen by the subjoined comparison.

Families. Germany. France.

Gramineæ. ¹⁄₁₃ ¹⁄₁₃

Umbelliferæ. ¹⁄₂₂ ¹⁄₂₁

Cruciferæ. ¹⁄₁₈ ¹⁄₁₉

Compositæ. ¹⁄₈ ¹⁄₇

Leguminosæ. ¹⁄₁₈ ¹⁄₁₆

Labiatæ. ¹⁄₂₆ ¹⁄₂₄

This agreement in the number of species in each family compared to the whole number of phenogamous species in the Floras of France and Germany, would not by any means exist if the German species which are missing in France were not replaced there by other types belonging to the same families. Those who are fond of imagining gradual transformations of species, and suppose the different kinds of parrots proper to two islands not far removed from each other to present examples of such a change, will be inclined to attribute the remarkable similarity between the two columns of figures which have just been given, to a migration of species, which, having been the same at first, have been altered gradually by the long-continued action of climatic causes during thousands of years, so that their identity being lost they appear to replace each other. But why is it that our common heather (Calluna vulgaris), why is it that our oaks have never advanced to the eastward of the Ural Mountains, and so passed from Europe to Northern Asia? Why is there no species of the genus Rosa in the Southern Hemisphere, and why are there scarcely any Calceolarias in the Northern Hemisphere? The necessary conditions of temperature are insufficient to explain this. Thermic relations alone cannot, any more than the hypothesis of migrations of plants radiating from certain central points, explain the present distribution of fixed organic forms. Thermic relations are hardly sufficient to explain the limits beyond which individual species do not pass, either in latitude towards the pole at the level of the sea, or in vertical elevation towards the summits of mountains. The cycle of vegetation in each species, however different its duration may be, requires, in order to be successfully passed through, a certain minimum of temperature. (Playfair, in the Transactions of the Royal Society of Edinburgh, vol. v. 1805, p. 202; Humboldt, on the sum of the degrees of temperature required for the cycle of vegetation in the Cerealia, in Mem. sur les lignes isothermes, p. 96; Boussingault, Economie rurale, T, ii. p. 659, 663, and 667; Alphonse Decandolle sur les causes qui limitent les espèces végétales, 1847, p. 8.) But all the conditions necessary for the existence of a plant, either as diffused naturally or by cultivation,—conditions of latitude or minimum distance from the pole, and of elevation or maximum height above the level of the sea,—are farther complicated by the difficulty of determining the commencement of the thermic cycle of vegetation, and by the influence which the unequal distribution of the same quantity of heat into groups of successive days and nights exercises on the excitability, the progressive development, and the whole vital process; to all this must be farther added hygrometric influences and those of atmospheric electricity.

My investigations respecting the numerical laws of the distribution of forms may possibly be applied at some future day with advantage to the different classes of Rotiferæ in the animal creation. The rich collections at the Museum d’Histoire Naturelle in the Jardin des Plantes at Paris, already contained, in 1820, (according to approximate estimations) above 56000 phænogamous and cryptogamous plants in herbariums, 44000 insects (a number doubtless too small, though given me by Latreille), 2500 species of fish, 700 reptiles, 4000 birds, and 500 mammalia. Europe has about 80 species of indigenous mammalia, 400 birds, and 30 reptiles. In the Northern temperate zone, therefore, the species of birds are five times more numerous than those of mammalia, as there are in Europe five times as many Compositæ as there are Amentaceæ and Coniferæ, and five times as many Leguminosæ as there are Orchideæ and Euphorbiaceæ. In the southern hemisphere the ratio of mammalia is in tolerably striking agreement, being as 1 to 4·3. Birds, and still more reptiles, increase in the number of species in approaching the torrid zone more than the mammalia. Cuvier’s researches might lead us to believe that the proportion was different in the earlier state of things, and that many more mammalia had perished by revolutions of Nature than birds. Latreille has shewn what groups of insects increase towards the pole, and what towards the equator. Illiger has given the countries of 3800 species of birds according to the quarters of the globe: it would have been much more instructive if the same thing had been done according to zones. We should find little difficulty in comprehending how on a given space of the earth’s surface the individuals of a class of plants or animals limit each other’s numbers, or how, after long continued contest and many fluctuations caused by the requirements of nourishment and mode of life, a state of equilibrium should be at last established; but the causes which have limited not the number of individuals of a form, but the forms themselves, in a particular space, and founded their typical diversity, are placed beneath the impenetrable veil which still conceals from our eyes all that relates to the manner of the first creation and commencement of organic beings.

If, then, we would attempt to solve the question spoken of in the early part of this dissertation, by giving in an approximate manner the numerical limit, (le nombre limite of French mathematicians), which the whole phanerogamæ now existing on the surface of the earth cannot be supposed to fall short of, we may perhaps find our safest guide in a comparison of the numerical ratios (which, as we have seen, may be assumed to exist between the different families of plants), with the number of species contained in herbariums and cultivated in our great botanic gardens. I have said that in 1820 the number of species contained in the herbariums of the Jardin des Plantes at Paris was already estimated at 56000. I do not permit myself to conjecture the amount which the herbariums of England may contain; but the great Paris herbarium, which was formed with much personal sacrifice by Benjamin Delessert, and given by him for free and general use, was stated at his death to contain 86000 species; a number almost equal to that which, as late as 1835, was conjecturally assigned by Lindley as that of all the species existing on the whole earth. (Lindley, Introduction to Botany, 2d edit. p. 504.) Few herbariums have been reckoned with care, after a complete and strict separation and withdrawal of all mere varieties. Not a few plants contained in smaller collections are still wanting in the greater herbariums which are supposed to be general or complete. Dr. Klotzsch estimates the present entire number of phænogamous plants in the great Royal Herbarium at Schöneberg, near Berlin, of which he is the curator, at 74000 species.

Loudon’s useful work, Hortus Britannicus, gives an approximate view of all the species which are, or at no remote time have been, cultivated in British gardens: the edition of 1832 enumerates, including indigenous plants, exactly 26660 phænogamous species. We must not confound with this large number of plants which have grown or been cultivated at any time and in any part of the whole British Islands, the number of living plants which can be shewn at any single moment of time in any single botanic garden. In this last-named respect the Botanic Garden of Berlin has long been regarded as one of the richest in Europe. The fame of its extraordinary riches rested formerly only on uncertain and approximate estimations, and, as my fellow-labourer and friend of many years’ standing, Professor Kunth, has justly remarked (in manuscript notices communicated to the Gartenbau-Verein in December 1846), “no real enumeration or computation could be made until a systematic catalogue, based on a rigorous examination of species, had been prepared. Such an enumeration has given rather above 14060 species: if we deduct from this number 375 cultivated Ferns, we have remaining 13685 phænogamous species; among which we find 1600 Compositæ, 1150 Leguminosæ, 428 Labiatæ, 370 Umbelliferæ, 460 Orchideæ, 60 Palms, and 600 Grasses and Cyperaceæ. If we compare with these numbers those of the species already described in recent works,—Compositæ (Decandolle and Walpers) about 10000; Leguminosæ, 8070; Labiatæ (Bentham), 2190; Umbelliferæ, 1620; Grasses, 3544; and Cyperaceæ (Kunth, Enumeratio Plantarum), 2000;—we shall perceive that the Berlin Botanic Garden cultivates, of the very large families (Compositæ, Leguminosæ, and Grasses), only 1-7th, 1-8th, and 1-9th;—and of the small families (Labiatæ and Umbelliferæ), about 1-5th, or 1-4th, of described species. If, then, we estimate the number of all the different phænogamous plants cultivated at one time in all the botanic gardens of Europe at 20000, we find that the cultivated species appear to be about the eighth part of those which are already either described or preserved in herbariums, and that these must nearly amount to 160000. This estimate need not be thought excessive, since of many of the larger families, (for example, Guttiferæ, Malpighiaceæ, Melastomeæ, Myrtaceæ, and Rubiaceæ), hardly a hundredth part are found in our garden.” If we take the number given by Loudon in his Hortus Britannicus (26660 species) as a basis, we shall find, (according to the justly drawn succession of inferences of Professor Kunth, in the manuscript notices from which I have borrowed the above), the estimate of 160000 species rise to 213000; and even this is still very moderate, for Heynhold’s Nomenclator botanicus hortensis (1846) even rates the phænogamous species then cultivated at 35600; whereas I have employed Loudon’s number for 1832, viz. 26660. On the whole it would appear from what has been said,—and the conclusion is at first sight a sufficiently striking one,—that at present there are almost more known species of phænogamous plants (with which we are acquainted by gardens, descriptions, or herbariums), than there are known insects. According to the average of the statements which I have received from several of our most distinguished entomologists whom I have had the opportunity of consulting, the number of insects at present described, or contained in collections without being described, may be taken at between 150000 and 170000 species. The rich Berlin collection does not contain less than 90000 species, among which are about 82000 Coleoptera. A very large number of plants have been collected in distant parts of the globe, without the insects which live on them or near them being brought at the same time. If, however, we limit the estimates of numbers to a single part of the world, and that the one which has been the best explored in respect to both plants and insects, viz. Europe, we find a very different proportion; for while we can hardly enumerate between seven and eight thousand European phænogamous plants, more than three times that number of European insects are already known. According to the interesting communications of my friend Dohrn at Stettin, 8700 insects have already been collected from the rich Fauna of that vicinity, (and many micro-Lepidopteræ are still wanting), while the phænogamous plants of the same district scarcely exceed 1000. The Insect Fauna of Great Britain is estimated at 11600 species. Such a preponderance of animal forms need the less surprise us, since large classes of insects subsist solely on animal substances, and others on agamous vegetation (funguses, and even those which are subterranean). Bombyx pini alone (the spider which infests the Scotch fir, and is the most destructive of all forest insects), is visited, according to Ratzeburg, by thirty-five parasitical Ichneumonides.

If these considerations have led us to the proportion borne by the species of plants cultivated in gardens to the entire amount of those which are already either described or preserved in herbariums, we have still to consider the proportion borne by the latter to what we conjecture to be the whole number of forms existing upon the earth at the present time; i. e. to test the assumed minimum of such forms by the relative numbers of species in the different families, therefore, by uncertain multipliers. Such a test, however, gives for the lowest limit or minimum number results so low as to lead us to perceive that even in the great families,—our knowledge of which has been of late most strikingly enriched by the descriptions of botanists,—we are still acquainted with only a small part of existing plants. The Repertorium of Walpers completes Decandolle’s Prodromus of 1825, up to 1846: we find in it, in the family of Leguminosæ, 8068 species. We may assume the ratio, or relative numerical proportion of this family to all phænogamous plants, to be ¹⁄₂₁—as we find it ¹⁄₁₀ within the tropics, ¹⁄₁₈ in the middle temperate, and ¹⁄₃₃ in the cold northern zone. The described Leguminosæ would thus lead us to assume only 169400 existing phænogamous species on the whole surface of the earth, whereas, as we have shewn, the Compositæ indicate more than 160000 already known species. The discordance is instructive, and may be further elucidated and illustrated by the following analogous considerations.

The major part of the Compositæ, of which Linnæus knew only 785 species and which has now grown to 12000, appear to belong to the Old Continent: at least Decandolle described only 3590 American, whilst the European, Asiatic, and African species amounted to 5093. This apparent richness in Compositæ is, however, illusive, and considerable only in appearance; the ratio or quotient of the family, (¹⁄₁₅ between the tropics, ¹⁄₇ in the temperate zone, and ¹⁄₁₃ in the cold zone), shews that even more species of Compositæ than Leguminosæ must hitherto have escaped the researches of travellers; for a multiplication by 12 would give us only the improbably low number of 144000 Phænogamous species. The families of Grasses and Cyperaceæ give still lower results, because comparatively still fewer of their species have been described and collected. We have only to cast our eyes on the map of South America, remembering the wide extent of territory occupied by grassy plains, not only in Venezuela and on the banks of the Apure and the Meta, but also to the south of the forest-covered regions of the Amazons, in Chaco, Eastern Tucuman, and the Pampas of Buenos Ayres and Patagonia, bearing in mind that of all these extensive regions the greater part have never been explored by botanists, and the remainder only imperfectly and incompletely so. Northern and Central Asia offer an almost equal extent of Steppes, but in which, however, dicotyledonous herbaceous plants are more largely mingled with the Gramineæ. If we had sufficient grounds for believing that we are now acquainted with half the phænogamous plants on the globe, and if we took the number of known species only at one or other of the before-mentioned numbers of 160000 or 213000, we should still have to take the number of grasses (the general proportion of which appears to be ¹⁄₁₂), in the first case at least at 26000, and in the second case at 35000 different species, which would give respectively in the two cases only either ¹⁄₈ or ¹⁄₁₀ part as known.

The assumption that we already know half the existing species of phænogamous plants is farther opposed by the following considerations. Several thousand species of Monocotyledons and Dycotyledons, and among them tall trees,—(I refer here to my own Expedition),—have been discovered in regions, considerable portions of which had been previously examined by distinguished botanists. The portions of the great continents which have never even been trodden by botanical observers considerably exceed in area those which have been traversed by such travellers, even in a superficial manner. The greatest variety of phænogamous vegetation, i. e. the greatest number of species on a given area, is found between the tropics, and in the sub-tropical zones. This last-mentioned consideration renders it so much the more important to remember how almost entirely unacquainted we are, on the New Continent, north of the equator, with the Floras of Oaxaca, Yucatan, Guatimala, Nicaragua, the Isthmus of Panama, Choco, Antioquia, and the Provincia de los Pastos;—and south of the equator, with the Floras of the vast forest region: between the Ucayale, the Rio de la Madera, and the Tocantin (three great tributaries of the Amazons), and with those of Paraguay and the Provincia de los Missiones. In Africa, except in respect to the coasts, we know nothing of the vegetation from 15° north to 20° south latitude; in Asia we are unacquainted with the Floras of the south and south-east of Arabia, where the highlands rise to about 6400 English feet above the level of the sea,—of the countries between the Thian-schan, the Kuenlün, and the Himalaya, all the west part of China, and the greater part of the countries beyond the Ganges. Still more unknown to the botanist are the interior of Borneo, New Guinea, and part of Australia. Farther to the south the number of species undergoes a wonderful diminution, as Joseph Hooker has well and ably shewn from his own observation in his Antarctic Flora. The three islands of which New Zealand consists extend from 34½° to 47¼° S. latitude, and as they contain, moreover, snowy mountains of above 8850 English feet elevation, they must include considerable diversity of climate. The Northern Island has been examined with tolerable completeness from the voyage of Banks and Solander to Lesson and the Brothers Cunningham and Colenso, and yet in more than 70 years we have only become acquainted with less than 700 phænogamous species. (Dieffenbach, Travels in New Zealand, 1843, vol. i. p. 419.) The paucity of vegetable corresponds to the paucity of animal species. Joseph Hooker, in his Flora Antarctica, p. 73-75, remarks that the “botany of the densely wooded regions of the Southern Islands of the New Zealand groups and of Fuegia is much more meagre not only than that of similarly clothed regions of Europe, but of islands many degrees nearer to the Northern pole than these are to the Southern one. Iceland, for instance, which is from 8 to 10 degrees farther from the equator than the Auckland and the Campbell Islands, contains certainly five times as many flowering plants. In the Antarctic Flora, under the influence of a cool and moist, but singularly equable climate, great uniformity, arising from paucity of species, is associated with great luxuriance of vegetation. This striking uniformity prevails both at different levels, (the species found on the plains appearing also on the slopes of the mountains), and over vast extents of country, from the south of Chili to Patagonia, and even to Tierra del Fuego, or from lat. 45° to 56°. Compare, on the other hand, in the northern temperate region, the Flora of the South of France, in the latitude of the Chonos Archipelago on the coast of Chili, with the Flora of Argyleshire in Scotland in the latitude of Cape Horn, and how great a difference of species is found; while in the Southern Hemisphere the same types of vegetation pass through many degrees of latitude. Lastly, on Walden Island, in lat. 80½° N., or not ten degrees from the North Pole of the earth, ten species of flowering plants have been collected, while in the southernmost islet of the South Shetlands, though only in lat. 63° S., only a solitary grass was found.” These considerations on the distribution of plants confirm the belief that the great mass of still unobserved, uncollected, and undescribed flowering plants must be sought for in tropical countries, and in the latitudes from 12° to 15° distant from the tropics.

It has appeared to me not unimportant to show the imperfect state of our knowledge in this still little cultivated department of arithmetical botany, and to propound numerical questions in a more distinct and determinate manner than could have been previously done. In all conjectures respecting numerical relations we must seek first for the possibility of deducing the lower or minimum limits; as in a question treated of by me elsewhere, on the proportion of coined gold and silver to the quantity of the precious metal fabricated in other ways; or as in the questions of how many stars, from the 10th to the 12th magnitude, are dispersed over the sky, and how many of the smallest telescopic stars the Milky Way may contain. (John Herschel, Results of Astron. Observ. at the Cape of Good Hope, 1847, p. 381.) We may consider it as established, that if it were possible to know completely and thoroughly by observation all the species belonging to one of the great families of phanerogamous or flowering plants, we should learn thereby at the same time, approximatively, the entire sum of all such plants (including all the families). As, therefore, by the progressive exploration of new countries we progressively and gradually exhaust the remaining unknown species of any of the great families, the previously assigned lowest limit rises gradually higher, and since the forms reciprocally limit each other in conformity with still undiscovered laws of universal organisation, we approach continually nearer to the solution of the great numerical problem of organic life. But is the number of organic forms itself a constant number? Do new vegetable forms spring from the ground after long periods of time, while others become more and more rare, and at last disappear? Geology, by means of her historical monuments of ancient terrestrial life, answers to the latter portion of this question affirmatively. “In the Ancient World,” to use the remark of an eminent naturalist, Link (Abhandl. der Akad. der Wiss. zu Berlin aus dem Jahr 1846, S. 322), “we see characters, now apparently remote and widely separated from each other, associated or crowded together in wondrous forms, as if a greater development and separation awaited a later age in the history of our planet.”